This site is dedicated to the mathematical and scientific study of ancient and modern structures, which traditionally have fallen under the category of “Sacred Geometry” or “pseudo-science.” This includes the geometric analysis of crop circles and megalithic monuments, as well as an exploration of the connections with fractals, harmonics and non-linear resonance.

Monday, December 22, 2014

I don’t have balls. I’ve never wanted them. I suspect most of
the crop circle hoaxers have them, along with an inversely proportional, large ego.

There is a group of people who live mostly in Wiltshire
England, and every year they create their own crop circle designs. Most of the
time the farmer is the victim in what is essentially an act of vandalism. There
are also rare instances when a farmer or company will commission a design. The
unwilling farmers, however, face damaged crop fields, as well as additional
damage caused by people wanting to come see the design. Researchers like me
face a corruption and muddying of the data.

When I first started studying the geometry of crop circles,
I wasted a lot of time studying hoaxed crop circles. A lot of time. A lot of
wasted time. I want to personally thank the hoaxers for wasting so much of my precious
research time, which I carved out of my daily life. It took me years to figure out the
difference between the hoaxed crop circles and the genuine ones. Now I don’t waste
as much time because I’ve developed a few geometric litmus tests that can be
used to spot the fakes and exclude them from the data pool.

So perhaps you understand my dilemma of whether to reveal
what I’ve learned in my nearly 5 years of crop circle research. If I teach the
hoaxers what I know, they can create better hoaxes and waste more of my time. I
am reluctant to publish specifics, but at the same time I am angry at myself
for self-censoring. Which brings me back to the point of this post: Crop Circle
Hoaxers Can Suck my Ovaries

I don’t think they are bad people, but they are misguided in
the belief that they are not harming their community. I suspect it is their disproportionally
large egos that have lead them astray. I don’t think it is about money. I don’t
see how one profits from faking crop circles. Some hoaxers believe their
circles are part of a dialog with the circle makers, and I say if you are that
compelled, find a place where you have permission, or choose a different medium
for your creative expression.

Here are a few general problems I’ve seen with the geometry
of hoaxed crop circle designs:

Inconsistent proportioning. The system of proportion varies
depending on which part of the design you look at.

Tram lines are used in the construction of the design
elements rather than integrated into the overall geometric design.

So my message to the hoaxers is as follows:

Knock it off; find a more productive hobby. You are muddying
the data and wasting the time of people who are trying to study the phenomenon
from a scientific/mathematical point of view. Stop harming those you should be
helping within your own community.

Sunday, December 21, 2014

Mathematics is a universal language, and our best way to
communicate with those who are very different from us. We see increasingly
complex mathematical designs appear in crop fields worldwide every year - in
grass, wheat, barley, corn, snow and ice (I call them all “crop circles” for
simplicity’s sake). Even the seemly simple ones hide a treasure of mathematics if
you dig below the surface. These crop circle designs have an underlying order and
beauty that even the mathematically challenged can appreciate.

It is my belief that these beautiful designs encode data, because
they contain blocks of objects that repeat, and there are rules about how the
blocks can be assembled. This basically describes how language works, so it’s
probable that these crop circle designs are using a geometric-based language. I
think of it as a geometric object-oriented programming language that may be
self-executing.

Let me clarify here that I am only talking about non-people-made
(NPM) crop circle designs. The designs made by people don’t follow the same
geometric rules, and have problems with proportion, scaling, and placement of
the designs with respect to tram lines. Some of you may be asking – if they’re
not made by people, then who? My answer to that is - an intelligent being who
knows more than I.

The Concept of Number

With the idea that math is universal, let’s start with
something basic like the concept of number. In the book Contact by Carl Sagan,
a radio transmitter on earth picked up a non-terrestrial signal with a series
of beeps and spaces that communicated intelligent knowledge of prime numbers. Suppose
we wanted to do something similar, except instead of using sound we wanted to
use a visual medium to transmit the first 7 prime numbers.

The best option for communicating numbers using geometric
figures would depend on how many spatial dimensions you have available to
communicate, and from which dimension the figures would be viewed from.

1-D

In one dimension (1-D), the best option to visually represent
number is a sequence of lines and spaces. A line of length 2 would be followed
by a space, then a line of length 3, followed by a space, etc… Note this would
need to be viewed from a 2-D perspective in order to decode the numbers.

Linear 1-D Representation of Prime Numbers

2-D

In two dimensions (2-D), the best option to visually represent
numbers is a sequence of circles, placed concentrically or within a 2-D
coordinate system. Radial lines on a polar coordinate system, triangles or
squares also provide other options, but circles are superior because of their
simplicity. Lines alone pose difficulty because of their 1-D nature. The line
would need to be thick enough to be seen, but then a second dimension is
introduced as well as a second number indicating the width. Using equilateral triangles
or squares to represent pure numbers is also possible, but practically
speaking, circles are still required to construct a perfect 60 or 90 degree
angle.

Circles are the best 2-D choice to represent number because:

A circle is defined by one number – its radius

A circle consists of one continuous line

All points on the circle are the same distance
from the center, which makes a circle resilient to distortion

Circles are the easiest geometric figure to
construct

The simplest, most elegant way to represent prime numbers in
2-D is with a sequence of concentric circles with radii (or diameters) measurements
equal to the prime numbers. Does this look familiar to anyone?

3-D

In three dimensions (3-D), the best option to visually represent
numbers is a sequence of spheres, placed concentrically or within a 3-D coordinate
system. It would be impossible, however, for a being living in 3-D to measure
the relative sizes of nested spheres, so this type of encoding is not ideal for us here in 3-space.

Conclusion

The circle is the best 2-D geometric representation of pure number, and the best visual representation of numbers for those of us living in 3 dimensions.

Now we have a starting point for our crop circle language. The
next logical step in decoding is to look at the sequences actually being
generated by the designs in our crops. Then comes the tricky task of nailing
down the positions of the design elements using a 2-D (polar?) coordinate
system.

About Me

The author has a B.A. degree in Mathematics from Humboldt State University. She has been a Peace Corps Volunteer in Nepal, and a high school geometry and calculus teacher. Most recently, she worked in the predictive modeling industry building statistical models that rank credit risk.